It has been common practice to secure rods in overlapped relationship by applying a clamping device functioning primarily to generate a substantial force holding the rods together in bearing engagement. The clamping forces are commonly generated by U-bolts embracing the rods, and traversing a plate forming a platform against which the U-bolts can be tightened. Reinforcing bars used in concrete structures have been secured by various forms of such clamping devices, which must be adapted to accommodate the standard ridged configuration on the surface of these rods. These ridges are formed in planes inclined to the axis of the rod, and commonly occur in planes of alternating inclination. Clamping devices for engaging such rods will preferably provide a corresponding inclination to the U-bolts, in arrangements such as those appearing in U.S. Pat. No. 3,771,884, issued to the present inventor. Since the stresses in such rods commonly approach the yield point of the rod material, it is desirable to utilize to as great a degree as possible the ridges on the rods as points for transfering the stresses. Prior devices, some of which have superficial appearances of similarity to the present invention, have not accomplished this utilization of the ridge configuration to the degree that has been found possible. Rods may be secured in overlapping relationship in situations where (a) both rods are concrete-reinforcing bars, and (b) one of the rods is a reinforcing bar, and the other rod secured to it has a smooth peripheral surface.